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arXiv:quant-ph/0007092 · Physics Letters A

Measurability of electromagnetic field: model and path integral methods

Horst-Heino von Borzeskowski, Michael B. Mensky

Published May 1, 1994• 11 citations
arXivHTMLPDF
DOI
10.1016/0375-9601(94)90447-2

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The description of interacting multilevel quantum system and quantum electromagnetic field in terms of statistical density matrix is considered in path integral approach. The statistical operator and probability transitions of quantum system are represented as mean of electromagnetic field influence functional. The influence functionals are defined for specific models of electromagnetic field. The explicit form for singleand multimode electromagnetic field is concretized in cases when initial state of the field is represented by vacuum and pure coherent.

Вестник Самарского государственного технического университета Серия Физико-математические науки•Jun 15, 2013•0 citations
Quantum restrictions on the measurability of an electromagnetic field strength and their relevance to the energy-time uncertainty relation are considered. The minimum errors in measuring electromagnetic field strengths, as they were estimated by the author (1988) in the framework of the phenomenological method of restricted path integral (RPI), are compared with the analogous estimates found by Landau and Peierls (1931) and by Bohr and Rosenfeld (1933) with the help of certain measurement setups. RPI-based restrictions, including those of Landau and Peierls as a special case, hold for any measuring schemes meeting the strict definition of measurement. Their fundamental nature is confirmed by the fact that their associated field detectability condition has the form of the energy-time uncertainty relation. The weaker restrictions suggested by Bohr and Rosenfeld rely on an extended definition of measurement. The energy?time uncertainty relation, which is the condition for the electromagnetic field to be detectable, is applied to the analysis of how the near-field scanning microscope works.
By formulating a path integral in the SU(2) fiber bundle space, a nonrelativistic spinor particle moving in external electromagnetic fields is studied. This formulation is a direct extension of Schulman’s [Phys. Rev. 176, 1588 (1968)] continuous treatment for spin; it unifies all spin states to a spherical top model. This theory enjoys a definite classical theory with spin–orbital interactions and the corresponding semiclassical approximation for the path integral. This method is also applicable to a particle moving in a more general Yang–Mills field.
The description of interacting multilevel quantum system and quantum electromagnetic field in terms of statistical density matrix is considered in path integral approach. The statistical operator and probability transitions of quantum system are represented as mean of electromagnetic field influence functional. The influence functionals are defined for specific models of electromagnetic field. The explicit form for singleand multimode electromagnetic field is concretized in cases when initial state of the field is represented by vacuum and pure coherent.